Baskerfield or variations isn't a common name, so it ought to be possible to put something together for them.
Ann Warren gives her birthplace as Bedford, Beds
WARNING. What follows is pure speculation
The only burial up to 1851 in Bedford of a possible parent is George Basterfield age 53 who was buried at Bedford St Paul on 13 Oct 1843
George Basterfield married Martha Cooper at Bedford St Paul on 13 Oct 1812
A member submission (not to be trusted) has a baptism at Campton on 6 June 1813 of Sarah Baskerfeild, daughter of George and Martha. There's a burial of Sarah Basterfield age 2 at Bedford St Paul on 21 May 1815.
In Bedford St Paul in 1841 was James Basterfield 30, Mary 35, George 11, Elizabeth 10.
I can't see George in 1841 though, nor can I see what happened to Martha (yet!)
So, so far everything is pointing to Bedford St Paul, with a possible link to Campton.
Could Ann have been the daughter of George and Martha and could she have been baptised at Campton whose post 1812 parish register hasn't been extracted onto either the IGI or BVRI? The same goes for James whose son was named George (after James' father?)
You need to check the marriage entry to Thomas Warren to see who the witnesses were. You also need to check Campton parish register for a possible baptism of Ann c1815. This can't be done online
David
